Polynomial Time Nondimensionalisation of Ordinary Differential Equations via their Lie Point Symmetries

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equation. We apply this principle by finding dilatations and translations that are Lie point symmetries of considered ordinary differential system. By rewriting original problem in an invariant coordinates set for these symmetries, one can reduce the involved number of parameters. This process is classically call nondimensionalisation in dimensional analysis. We present an algorithm based on this standpoint and show that its arithmetic complexity is polynomial in input's size

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Area efficient parallel lfsr for cyclic redundancy check

Cyclic Redundancy Check (CRC), code for error detection finds many applications in the field of digital communication, data storage, control system and data compression. CRC encoding operation is carried out by using a Linear Feedback Shift Register (LFSR). Serial implementation of CRC requires more clock cycles which is equal to data message length plus generator polynomial degree but in parallel implementation of CRC one clock cycle is required if a whole data message is applied at a time. In previous work related to parallel LFSR, hardware complexity of the architecture reduced using a technique named state space transformation. This paper presents detailed explaination of search algorithm implementation and technique to find number of XOR gates required for different CRC algorithms. This paper presents a searching algorithm and new technique to find the number of XOR gates required for different CRC algorithms. The comparison between proposed and previous architectures shows that the number of XOR gates are reduced for CRC algorithms which improve the hardware efficiency. Searching algorithm and all the matrix computations have been performed using MATLAB simulations